Problem: There are 7 people in a room. If everyone shakes everyone else's hand exactly once, how many handshakes occur?
Solution: Given 7 people, each person shakes the hands of 6 other people. The following is almost the answer. $7 \times 6 = 42$ We have double counted the handshakes though, since Nadia shaking Ben's hand is the same handshake as Ben shaking Nadia's hand. Therefore, the following is the correct answer. $\dfrac{7 \times 6}{2} = 21$